Characters of odd degree

Gunter Malle; Britta Späth

doi:https://doi.org/10.4007/annals.2016.184.3.6

Abstract

We prove the McKay conjecture on characters of odd degree. A major step in the proof is the verification of the inductive McKay condition for groups of Lie type and primes $\ell$ such that a Sylow $\ell$-subgroup or its maximal normal abelian subgroup is contained in a maximally split torus by means of a new equivariant version of Harish-Chandra induction. Specifics of characters of odd degree, namely, that most of them lie in the principal Harish-Chandra series, then allow us to deduce from it the McKay conjecture for the prime $2$, hence for characters of odd degree.

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[Bo05] $Go to document$ C. Bonnafé, "Quasi-isolated elements in reductive groups," Comm. Algebra, vol. 33, iss. 7, pp. 2315-2337, 2005.

Show bibtex

@ARTICLE{Bo05, mrkey = {2153225}, number = {7}, issn = {0092-7872}, author = {Bonnaf{é}, C{é}dric}, mrclass = {20G15}, doi = {10.1081/AGB-200063602}, journal = {Comm. Algebra}, zblnumber = {1096.20037}, volume = {33}, mrnumber = {2153225}, fjournal = {Communications in Algebra}, mrreviewer = {Evgenii L. Bashkirov}, coden = {COALDM}, title = {Quasi-isolated elements in reductive groups}, year = {2005}, pages = {2315--2337}, }
[Cedric] C. Bonnafé, Sur les Caractères des Groupes Réductifs finis à Centre Non Connexe: Applications aux Groupes Spéciaux Linéaires et Unitaires, Paris: Math. Soc. France, 2006, vol. 306.

Show bibtex

@BOOK{Cedric, mrkey = {2274998}, issn = {0303-1179}, author = {Bonnaf{é}, C{é}dric}, mrclass = {20G40 (20G05)}, series = {Astérisque}, address = {Paris}, publisher = {Math. Soc. France}, zblnumber = {1157.20022}, volume = {306}, mrnumber = {2274998}, fjournal = {Astérisque}, mrreviewer = {Robert B{é}dard}, title = {Sur les Caractères des Groupes Réductifs finis à Centre Non Connexe: Applications aux Groupes Spéciaux Linéaires et Unitaires}, year = {2006}, pages = {vi+165}, }
[BM92] $Go to document$ M. Broué and G. Malle, "Théorèmes de Sylow génériques pour les groupes réductifs sur les corps finis," Math. Ann., vol. 292, iss. 2, pp. 241-262, 1992.

Show bibtex

@ARTICLE{BM92, mrkey = {1149033}, number = {2}, issn = {0025-5831}, author = {Brou{é}, Michel and Malle, Gunter}, mrclass = {20G40}, doi = {10.1007/BF01444619}, journal = {Math. Ann.}, zblnumber = {0820.20057}, volume = {292}, mrnumber = {1149033}, fjournal = {Mathematische Annalen}, mrreviewer = {Bhama Srinivasan}, coden = {MAANA}, title = {Théorèmes de {S}ylow génériques pour les groupes réductifs sur les corps finis}, year = {1992}, pages = {241--262}, }
[BMM] M. Broué, G. Malle, and J. Michel, "Generic blocks of finite reductive groups," in Représentations Unipotentes Génériques et Blocs des Groupes Réductifs Finis, Paris: Math. Soc. France, 1993, vol. 212, pp. 7-92.

Show bibtex

@INCOLLECTION{BMM, mrkey = {1235832}, issn = {0303-1179}, author = {Brou{é}, Michel and Malle, Gunter and Michel, Jean}, mrclass = {20G05 (20C20)}, series = {Astérisque}, address = {Paris}, publisher = {Math. Soc. France}, zblnumber = {0843.20012}, volume = {212}, mrnumber = {1235832}, booktitle = {Repr{é}sentations Unipotentes G{é}n{é}riques et Blocs des Groupes R{é}ductifs Finis}, fjournal = {Astérisque}, mrreviewer = {Bhama Srinivasan}, title = {Generic blocks of finite reductive groups}, year = {1993}, pages = {7--92}, }
[CE04] $Go to document$ M. Cabanes and M. Enguehard, Representation Theory of Finite Reductive Groups, Cambridge: Cambridge Univ. Press, 2004, vol. 1.

Show bibtex

@BOOK{CE04, mrkey = {2057756}, author = {Cabanes, Marc and Enguehard, Michel}, mrclass = {20G05 (20G40)}, series = {New Mathematical Monographs}, isbn = {0-521-82517-2}, address = {Cambridge}, publisher = {Cambridge Univ. Press}, doi = {10.1017/CBO9780511542763}, zblnumber = {1069.20032}, volume = {1}, mrnumber = {2057756}, mrreviewer = {Bhama Srinivasan}, title = {Representation Theory of Finite Reductive Groups}, year = {2004}, pages = {xviii+436}, }
[CS13] $Go to document$ M. Cabanes and B. Späth, "Equivariance and extendibility in finite reductive groups with connected center," Math. Z., vol. 275, iss. 3-4, pp. 689-713, 2013.

Show bibtex

@ARTICLE{CS13, mrkey = {3127033}, number = {3-4}, issn = {0025-5874}, author = {Cabanes, Marc and Sp{ä}th, Britta}, mrclass = {20C33 (20C15 20C20 20D06 20G40)}, doi = {10.1007/s00209-013-1156-7}, journal = {Math. Z.}, zblnumber = {1328.20019}, volume = {275}, mrnumber = {3127033}, fjournal = {Mathematische Zeitschrift}, mrreviewer = {George J. McNinch}, title = {Equivariance and extendibility in finite reductive groups with connected center}, year = {2013}, pages = {689--713}, }
[CS15] M. Cabanes and B. Späth, "Equivariant character correspondences and inductive McKay condition for type A," J. reine angew. Math., 2016.

Show bibtex

@article{CS15, author = {Cabanes, Marc and Sp{ä}th, Britta}, TITLE = {Equivariant character correspondences and inductive {M}c{K}ay condition for type {A}}, journal = {J. reine angew. Math.}, note={to appear}, year = {2016}, }
[Ca85] R. W. Carter, Finite Groups of Lie Type. Conjugacy classes and complex characters, New York: John Wiley & Sons, 1985.

Show bibtex

@BOOK{Ca85, mrkey = {0794307}, author = {Carter, Roger W.}, mrclass = {20G40 (20-02 20C15)}, series = {Pure Appl. Math.}, isbn = {0-471-90554-2}, address = {New York}, publisher = {John Wiley \& Sons}, mrnumber = {0794307}, mrreviewer = {David B. Surowski}, zblnumber = {0567.20023}, title = {Finite Groups of {L}ie Type. Conjugacy classes and complex characters}, year = {1985}, pages = {xii+544}, }
[DM] $Go to document$ F. Digne and J. Michel, Representations of Finite Groups of Lie Type, Cambridge: Cambridge Univ. Press, 1991, vol. 21.

Show bibtex

@BOOK{DM, mrkey = {1118841}, author = {Digne, Fran{ç}ois and Michel, Jean}, mrclass = {20G05 (20-02 20C33 20G40)}, series = {London Math. Soc. Stud. Texts}, isbn = {0-521-40117-8; 0-521-40648-X}, address = {Cambridge}, publisher = {Cambridge Univ. Press}, doi = {10.1017/CBO9781139172417}, zblnumber = {0815.20014}, volume = {21}, mrnumber = {1118841}, mrreviewer = {Bhama Srinivasan}, title = {Representations of Finite Groups of {L}ie Type}, year = {1991}, pages = {iv+159}, }
[DD93] $Go to document$ R. Dipper and J. Du, "Harish-Chandra vertices," J. Reine Angew. Math., vol. 437, pp. 101-130, 1993.

Show bibtex

@ARTICLE{DD93, mrkey = {1212254}, issn = {0075-4102}, author = {Dipper, Richard and Du, Jie}, mrclass = {20C20}, doi = {10.1515/crll.1993.437.101}, journal = {J. Reine Angew. Math.}, zblnumber = {0768.20004}, volume = {437}, mrnumber = {1212254}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, mrreviewer = {Bhama Srinivasan}, title = {Harish-{C}handra vertices}, year = {1993}, pages = {101--130}, }
[GeckHC] $Go to document$ M. Geck, "A note on Harish-Chandra induction," Manuscripta Math., vol. 80, iss. 4, pp. 393-401, 1993.

Show bibtex

@ARTICLE{GeckHC, mrkey = {1243154}, number = {4}, issn = {0025-2611}, author = {Geck, Meinolf}, mrclass = {20C33 (20G05)}, doi = {10.1007/BF03026560}, journal = {Manuscripta Math.}, zblnumber = {0821.20027}, volume = {80}, mrnumber = {1243154}, fjournal = {Manuscripta Mathematica}, mrreviewer = {Robert B. Howlett}, coden = {MSMHB2}, title = {A note on {H}arish-{C}handra induction}, year = {1993}, pages = {393--401}, }
[GP] M. Geck and G. Pfeiffer, Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, New York: The Clarendon Press, Oxford University Press, 2000.

Show bibtex

@BOOK{GP, mrkey = {1778802}, author = {Geck, Meinolf and Pfeiffer, G{ö}tz}, mrclass = {20C15 (20C08 20F55)}, series = {London Math. Soc. Monogr.}, isbn = {0-19-850250-8}, publisher = {The Clarendon Press, Oxford University Press}, zblnumber = {0996.20004}, address = {New York}, mrnumber = {1778802}, mrreviewer = {Jian-yi Shi}, title = {Characters of Finite {C}oxeter {G}roups and {I}wahori-{H}ecke Algebras}, year = {2000}, pages = {xvi+446}, }
[GLS3] $Go to document$ D. Gorenstein, R. Lyons, and R. Solomon, The Classification of the Finite Simple Groups, Providence, RI: Amer. Math. Soc., 1994, vol. 40.

Show bibtex

@BOOK{GLS3, mrkey = {1303592}, author = {Gorenstein, Daniel and Lyons, Richard and Solomon, Ronald}, mrclass = {20D05 (20-02)}, series = {Math. Surveys Monogr.}, isbn = {0-8218-0334-4}, address = {Providence, RI}, publisher = {Amer. Math. Soc.}, doi = {10.1090/surv/040.1}, zblnumber = {0816.20016}, volume = {40}, mrnumber = {1303592}, mrreviewer = {J. L. Alperin}, title = {The Classification of the Finite Simple Groups}, year = {1994}, pages = {xiv+165}, }
[HL] $Go to document$ R. B. Howlett and G. I. Lehrer, "Induced cuspidal representations and generalised Hecke rings," Invent. Math., vol. 58, iss. 1, pp. 37-64, 1980.

Show bibtex

@ARTICLE{HL, mrkey = {0570873}, number = {1}, issn = {0020-9910}, author = {Howlett, R. B. and Lehrer, G. I.}, mrclass = {20C15 (20G40)}, doi = {10.1007/BF01402273}, journal = {Invent. Math.}, zblnumber = {0435.20023}, volume = {58}, mrnumber = {0570873}, fjournal = {Inventiones Mathematicae}, mrreviewer = {Bhama Srinivasan}, coden = {INVMBH}, title = {Induced cuspidal representations and generalised {H}ecke rings}, year = {1980}, pages = {37--64}, }
[HL83] $Go to document$ R. B. Howlett and G. I. Lehrer, "Representations of generic algebras and finite groups of Lie type," Trans. Amer. Math. Soc., vol. 280, iss. 2, pp. 753-779, 1983.

Show bibtex

@ARTICLE{HL83, mrkey = {0716849}, number = {2}, issn = {0002-9947}, author = {Howlett, R. B. and Lehrer, G. I.}, mrclass = {20G05 (16A64 16A65)}, doi = {10.2307/1999645}, journal = {Trans. Amer. Math. Soc.}, zblnumber = {0537.20018}, volume = {280}, mrnumber = {0716849}, fjournal = {Transactions of the American Mathematical Society}, mrreviewer = {S. Yu. Prishepionok}, coden = {TAMTAM}, title = {Representations of generic algebras and finite groups of {L}ie type}, year = {1983}, pages = {753--779}, }
[HL94] $Go to document$ R. B. Howlett and G. I. Lehrer, "On Harish-Chandra induction and restriction for modules of Levi subgroups," J. Algebra, vol. 165, iss. 1, pp. 172-183, 1994.

Show bibtex

@ARTICLE{HL94, mrkey = {1272585}, number = {1}, issn = {0021-8693}, author = {Howlett, R. B. and Lehrer, G. I.}, mrclass = {20C33 (20C20)}, doi = {10.1006/jabr.1994.1104}, journal = {J. Algebra}, zblnumber = {0802.20036}, volume = {165}, mrnumber = {1272585}, fjournal = {Journal of Algebra}, mrreviewer = {Peter Fleischmann}, coden = {JALGA4}, title = {On {H}arish-{C}handra induction and restriction for modules of {L}evi subgroups}, year = {1994}, pages = {172--183}, }
[Hu] $Go to document$ B. Huppert, Character Theory of Finite Groups, Berlin: Walter de Gruyter & Co., 1998.

Show bibtex

@BOOK{Hu, mrkey = {1645304}, number = {25}, author = {Huppert, Bertram}, mrclass = {20C15 (20C05 20C10)}, series = {de Gruyter Exp. Math.}, isbn = {3-11-015421-8}, address = {Berlin}, publisher = {Walter de Gruyter \& Co.}, doi = {10.1515/9783110809237}, zblnumber = {0932.20007}, mrnumber = {1645304}, mrreviewer = {Gerhard Hiss}, title = {Character Theory of Finite Groups}, year = {1998}, pages = {vi+618}, }
[Isa] M. I. Isaacs, Character Theory of Finite Groups, New York: Academic Press [Harcourt Brace Jovanovich, Publishers], 1976, vol. 69.

Show bibtex

@BOOK{Isa, mrkey = {0460423}, author = {Isaacs, I. Martin}, mrclass = {20-02}, series = {Pure Appl. Math.}, address = {New York}, publisher = {Academic Press [Harcourt Brace Jovanovich, Publishers]}, volume = {69}, mrnumber = {0460423}, mrreviewer = {Stephen D. Smith}, zblnumber = {0337.20005}, title = {Character Theory of Finite Groups}, year = {1976}, pages = {xii+303}, }
[IMN] $Go to document$ M. I. Isaacs, G. Malle, and G. Navarro, "A reduction theorem for the McKay conjecture," Invent. Math., vol. 170, iss. 1, pp. 33-101, 2007.

Show bibtex

@ARTICLE{IMN, mrkey = {2336079}, number = {1}, issn = {0020-9910}, author = {Isaacs, I. Martin and Malle, Gunter and Navarro, Gabriel}, mrclass = {20C20 (20C33 20C34)}, doi = {10.1007/s00222-007-0057-y}, journal = {Invent. Math.}, zblnumber = {1138.20010}, volume = {170}, mrnumber = {2336079}, fjournal = {Inventiones Mathematicae}, mrreviewer = {Charles W. Eaton}, coden = {INVMBH}, title = {A reduction theorem for the {M}c{K}ay conjecture}, year = {2007}, pages = {33--101}, }
[Lu] G. Lusztig, Characters of Reductive Groups over a Finite Field, Princeton, NJ: Princeton Univ. Press, 1984, vol. 107.

Show bibtex

@BOOK{Lu, mrkey = {0742472}, author = {Lusztig, George}, mrclass = {20G05 (14L20 20C15)}, series = {Ann. of Math. Stud.}, isbn = {0-691-08350-9; 0-691-08351-7}, address = {Princeton, NJ}, publisher = {Princeton Univ. Press}, zblnumber = {0556.20033}, volume = {107}, mrnumber = {0742472}, mrreviewer = {Bhama Srinivasan}, title = {Characters of Reductive Groups over a Finite Field}, year = {1984}, pages = {xxi+384}, }
[LuDis] G. Lusztig, "On the representations of reductive groups with disconnected centre," in Orbites Unipotentes et Représentations, I, Paris: Math. Soc. France, 1988, vol. 168, p. 10, 157-166.

Show bibtex

@incollection{LuDis, mrkey = {1021495}, issn = {0303-1179}, author = {Lusztig, George}, mrclass = {20G05 (20G40)}, series = {Astérisque}, address = {Paris}, publisher = {Math. Soc. France}, volume = {168}, mrnumber = {1021495}, booktitle = {Orbites Unipotentes et Repr{é}sentations, I}, mrreviewer = {Robert B{é}dard}, title = {On the representations of reductive groups with disconnected centre}, year = {1988}, pages = {10, 157--166}, }
[MaH0] $Go to document$ G. Malle, "Height 0 characters of finite groups of Lie type," Represent. Theory, vol. 11, pp. 192-220, 2007.

Show bibtex

@ARTICLE{MaH0, mrkey = {2365640}, issn = {1088-4165}, author = {Malle, Gunter}, mrclass = {20C33 (20G40)}, doi = {10.1090/S1088-4165-07-00312-3}, journal = {Represent. Theory}, zblnumber = {1139.20008}, volume = {11}, mrnumber = {2365640}, fjournal = {Representation Theory. An Electronic Journal of the American Mathematical Society}, mrreviewer = {Gerhard Hiss}, title = {Height 0 characters of finite groups of {L}ie type}, year = {2007}, pages = {192--220}, }
[ManonLie] $Go to document$ G. Malle, "The inductive McKay condition for simple groups not of Lie type," Comm. Algebra, vol. 36, iss. 2, pp. 455-463, 2008.

Show bibtex

@ARTICLE{ManonLie, mrkey = {2387535}, number = {2}, issn = {0092-7872}, author = {Malle, Gunter}, mrclass = {20C15 (20C33 20C34)}, doi = {10.1080/00927870701716090}, journal = {Comm. Algebra}, zblnumber = {1153.20009}, volume = {36}, mrnumber = {2387535}, fjournal = {Communications in Algebra}, mrreviewer = {A. S. Kondrat{\cprime}ev}, coden = {COALDM}, title = {The inductive {M}c{K}ay condition for simple groups not of {L}ie type}, year = {2008}, pages = {455--463}, }
[MaExt] $Go to document$ G. Malle, "Extensions of unipotent characters and the inductive McKay condition," J. Algebra, vol. 320, iss. 7, pp. 2963-2980, 2008.

Show bibtex

@ARTICLE{MaExt, mrkey = {2442005}, number = {7}, issn = {0021-8693}, author = {Malle, Gunter}, mrclass = {20C33 (20C15)}, doi = {10.1016/j.jalgebra.2008.06.033}, journal = {J. Algebra}, zblnumber = {1163.20003}, volume = {320}, mrnumber = {2442005}, fjournal = {Journal of Algebra}, mrreviewer = {A. S. Kondrat{\cprime}ev}, coden = {JALGA4}, title = {Extensions of unipotent characters and the inductive {M}c{K}ay condition}, year = {2008}, pages = {2963--2980}, }
[MT] $Go to document$ G. Malle and D. Testerman, Linear Algebraic Groups and Finite Groups of Lie Type, Cambridge: Cambridge Univ. Press, 2011, vol. 133.

Show bibtex

@BOOK{MT, mrkey = {2850737}, author = {Malle, Gunter and Testerman, Donna}, mrclass = {20G15 (20D06 20G05)}, series = {Cambridge Studies in Advanced Mathematics}, isbn = {978-1-107-00854-0}, address = {Cambridge}, publisher = {Cambridge Univ. Press}, doi = {10.1017/CBO9780511994777}, zblnumber = {1256.20045}, volume = {133}, mrnumber = {2850737}, mrreviewer = {Timothy C. Burness}, title = {Linear Algebraic Groups and Finite Groups of {L}ie Type}, year = {2011}, pages = {xiv+309}, }
[McGovern] $Go to document$ K. McGovern, "Multiplicities of principal series representations of finite groups with split $(B,\,N)$-pairs," J. Algebra, vol. 77, iss. 2, pp. 419-442, 1982.

Show bibtex

@ARTICLE{McGovern, mrkey = {0673126}, number = {2}, issn = {0021-8693}, author = {McGovern, Kathy}, mrclass = {20G05}, doi = {10.1016/0021-8693(82)90264-2}, journal = {J. Algebra}, zblnumber = {0492.20023}, volume = {77}, mrnumber = {0673126}, fjournal = {Journal of Algebra}, mrreviewer = {Louis Solomon}, title = {Multiplicities of principal series representations of finite groups with split {$(B,\,N)$}-pairs}, year = {1982}, pages = {419--442}, }
[McK] $Go to document$ J. McKay, "Irreducible representations of odd degree," J. Algebra, vol. 20, pp. 416-418, 1972.

Show bibtex

@ARTICLE{McK, mrkey = {0286904}, issn = {0021-8693}, author = {McKay, John}, mrclass = {20.80}, doi = {10.1016/0021-8693(72)90066-X}, journal = {J. Algebra}, zblnumber = {0235.20009}, volume = {20}, mrnumber = {0286904}, fjournal = {Journal of Algebra}, mrreviewer = {J. S. Frame}, title = {Irreducible representations of odd degree}, year = {1972}, pages = {416--418}, }
[NT15] $Go to document$ G. Navarro and P. H. Tiep, "Irreducible representations of odd degree," Math. Ann., vol. 365, pp. 1155-1185, 2016.

Show bibtex

@ARTICLE{NT15, author = {Navarro, G. and Tiep, P. H.}, journal = {Math.~Ann.}, volume = {365}, pages = {1155--1185}, title = {Irreducible representations of odd degree}, year = {2016}, doi = {10.1007/s00208-015-1334-5}, MRNUMBER={3521086}, }
[Sp_Diss] $Go to document$ B. Späth, Die McKay-Vermutung für quasi-einfache Gruppen vom Lie-Typ.

Show bibtex

@MISC{Sp_Diss, author = {Sp{ä}th, Britta}, note = {dissertation, {TU K}aiserslautern}, url = {http://kluedo.ub.uni-kl.de/volltexte/2007/2073/pdf/Spaeth\_McKay.pdf}, title = {Die {M}cKay-{V}ermutung für quasi-einfache {G}ruppen vom {L}ie-{T}yp}, }
[Sp09] $Go to document$ B. Späth, "The McKay conjecture for exceptional groups and odd primes," Math. Z., vol. 261, iss. 3, pp. 571-595, 2009.

Show bibtex

@ARTICLE{Sp09, mrkey = {2471089}, number = {3}, issn = {0025-5874}, author = {Sp{ä}th, Britta}, mrclass = {20C20 (20G40)}, doi = {10.1007/s00209-008-0340-7}, journal = {Math. Z.}, zblnumber = {1178.20006}, volume = {261}, mrnumber = {2471089}, fjournal = {Mathematische Zeitschrift}, mrreviewer = {Stuart Martin}, coden = {MAZEAX}, title = {The {M}c{K}ay conjecture for exceptional groups and odd primes}, year = {2009}, pages = {571--595}, }
[Sp13] $Go to document$ B. Späth, "A reduction theorem for the Alperin-McKay conjecture," J. Reine Angew. Math., vol. 680, pp. 153-189, 2013.

Show bibtex

@ARTICLE{Sp13, mrkey = {3100954}, issn = {0075-4102}, author = {Sp{ä}th, Britta}, mrclass = {20C20 (20C15 20C33)}, doi = {10.1515/crelle.2012.035}, journal = {J. Reine Angew. Math.}, zblnumber = {1283.20006}, volume = {680}, mrnumber = {3100954}, fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]}, mrreviewer = {Burkhard K{ü}lshammer}, title = {A reduction theorem for the {A}lperin-{M}c{K}ay conjecture}, year = {2013}, pages = {153--189}, }
[Spaeth2] $Go to document$ B. Späth, "Sylow $d$-tori of classical groups and the McKay conjecture. I," J. Algebra, vol. 323, iss. 9, pp. 2469-2493, 2010.

Show bibtex

@ARTICLE{Spaeth2, mrkey = {2602390}, number = {9}, issn = {0021-8693}, author = {Sp{ä}th, Britta}, mrclass = {20C33 (20C20 20G05 20G40)}, doi = {10.1016/j.jalgebra.2010.02.008}, journal = {J. Algebra}, zblnumber = {1260.20015}, volume = {323}, mrnumber = {2602390}, fjournal = {Journal of Algebra}, mrreviewer = {George J. McNinch}, coden = {JALGA4}, title = {Sylow {$d$}-tori of classical groups and the {M}c{K}ay conjecture. {I}}, year = {2010}, pages = {2469--2493}, }
[Sp12] $Go to document$ B. Späth, "Inductive McKay condition in defining characteristic," Bull. Lond. Math. Soc., vol. 44, iss. 3, pp. 426-438, 2012.

Show bibtex

@ARTICLE{Sp12, mrkey = {2966987}, number = {3}, issn = {0024-6093}, author = {Sp{ä}th, Britta}, mrclass = {20C33 (20C15)}, doi = {10.1112/blms/bdr100}, journal = {Bull. Lond. Math. Soc.}, zblnumber = {1251.20020}, volume = {44}, mrnumber = {2966987}, fjournal = {Bulletin of the London Mathematical Society}, mrreviewer = {Hung Phi Tong-Viet}, title = {Inductive {M}c{K}ay condition in defining characteristic}, year = {2012}, pages = {426--438}, }
[Springer] $Go to document$ T. A. Springer, "Regular elements of finite reflection groups," Invent. Math., vol. 25, pp. 159-198, 1974.

Show bibtex

@ARTICLE{Springer, mrkey = {0354894}, issn = {0020-9910}, author = {Springer, T. A.}, mrclass = {20H15}, doi = {10.1007/BF01390173}, journal = {Invent. Math.}, zblnumber = {0287.20043}, volume = {25}, mrnumber = {0354894}, fjournal = {Inventiones Mathematicae}, mrreviewer = {R. Steinberg}, title = {Regular elements of finite reflection groups}, year = {1974}, pages = {159--198}, }
[Tits] $Go to document$ J. Tits, "Normalisateurs de tores. I. Groupes de Coxeter étendus," J. Algebra, vol. 4, pp. 96-116, 1966.

Show bibtex

@ARTICLE{Tits, mrkey = {0206117}, issn = {0021-8693}, author = {Tits, J.}, mrclass = {20.75}, doi = {10.1016/0021-8693(66)90053-6}, journal = {J. Algebra}, zblnumber = {0145.24703}, volume = {4}, mrnumber = {0206117}, fjournal = {Journal of Algebra}, mrreviewer = {Rimhak Ree}, title = {Normalisateurs de tores. {I}. {G}roupes de {C}oxeter étendus}, year = {1966}, pages = {96--116}, }

Characters of odd degree

Abstract

Authors